Let's say we want to compute cot(0.0015) as accurately as possible using the following table by a) interpolating for cot(a), b) by interpolating for cos(r) and sin(x) and using them to calculate cot(x). Also, estimate the error in b) and explain the difference in a) and b). Here is the table

 

sin r Cos z cot a 0.001 0.001000 1.000000 1000.0 0.002 0.002000 0.999998 499.999 0.003 0.003000 0.999996 333.332 0.004 0.004000 0.999992 249.999 0.005 0.005000 0.999988 199.998